Question

Solve the equations x + y = 4 and 2x - y = 5 using the method of reduction.

Answer 1

The given equations can be considered in the matrix equation as

AX = B

i.e `[(1,1), (2,-1)] [(x), (y)] = [(4),(5)]`

Apply R₂ - 2R₁ 

`[(1,1), (0,-3)] [(x),(y)] = [(4),(-3)]`

`[(x + y), (-3y)] = [(4),(-3)]`

By equality of matrices

x + y = 4,              -3y = -3

x = 3                       y = 1